1. Field of the Invention
The present application relates to a method and an apparatus for controlling exposure of a surface of a substrate. In particular, the present invention relates to an improved CD control (CD=Critical Dimension) in micro lithography pattern generators using spatial light modulators (SLM).
2. Description of the Related Art:
The prior art basically describes two different approaches for implementing a pattern generator using a SLM for generating a pattern to be transferred to a surface of a substrate.
The first approach uses large pixel deflections, i.e., the deflection is large when compared to the radiation wavelength used. Further, a substantially digital, i.e., on and off, addressing is used. An example for this first approach is the Texas Instrument's DLP chip with deflection angles of +/−10°. With a pixel grid size of 17 μm the system can be described by classical light rays which are reflected by the individual pixels either into a projection lens (bright spot) or to an absorber (dark spot). Grey pixels can be obtained by time multiplexing for continuous light sources, and by multiple exposures for pulsed light sources.
The second approach uses a deflection at about half the radiation wavelength and an analog addressing. For this approach the SLM is described as a phase grating causing interference. Reflected light is only found in discrete diffraction orders. Conventionally, such a micro lithography pattern generator having a SLM uses the zero order to generate a pattern. That is bright spots are obtained for non-deflected pixels, and dark spots are obtained for deflected pixels. Grey pixels can be generated in one light pulse by partial deflection.
In micro lithography pattern generators grey pixels are needed to obtain an addressing grid finer than the projected pixel grid. The exact grey level has to be controlled very tightly as it directly affects the uniformity of the critical dimension (CD) which is one of the most important performance parameters of micro lithography pattern generators.
The above described first prior art approach is disadvantageous in that a large amount of time for the multiple exposures is required. This reduces the throughput, a second very important performance parameter of micro lithography pattern generators. Patterning the substrates using analog addressing but still with a large deflection would cure this disadvantage. However, the precision requirements in the deflection control can not be met as the intensity in the generated image changes very quickly in a small fraction of the deflection addressing range. Even worse, the non-symmetrical illumination of the projection optics for grey pixels ruins CD control completely, even for minute focus errors.
The above described second prior art approach works good for ideally flat pixels, e.g., for ideally flat micro-mirrors in a SLM. CD control is very good, and the CD is a smooth, though nonlinear function of the intensity reflected from the pixel (mirror), the reflected intensity, again, being a smooth but non-linear function of the deflection as is shown in FIG. 5. FIG. 5 is a graph of the relative intensity versus the relative deflection of a mirror of the SLM, i.e., the relative intensity of light at a predetermined pixel on a substrate to be patterned in response to a specific deflection of the mirror. As can be seen, the first maximum 50 of the intensity is obtained when the relative deflection is zero, and the first minimum 52 of the intensity is obtained when the relative deflection is one. Also a second maximum and a second minimum are shown. As can be seen from FIG. 5, binary switching of intensity between maximum and zero intensity can be simply achieved by switching deflection between zero deflection and a relative deflection of one. The maximum intensity decreases rapidly with growing deflection. Therefore, alternatively, any large relative deflection may be used for producing (near) zero intensity. As can be further seen from FIG. 5, by using the second prior art approach, a continuous change in intensity from nominal dose (maximum dose or relative intensity one) to zero (reached at a relative deflection one or nominal deflection) can be obtained.
A disadvantage when producing grey levels arises from pixels (mirrors) which are not perfectly flat. FIG. 6 shows the relative intensity versus the relative deflection for pixels (mirrors) having a bend or non-planarity. For clarity, the non-planarity is quite strong, and as can be seen, the intensity in the first maximum 50 is lower than shown in FIG. 5. More importantly, the first minimum 52 does not reach zero intensity any more. This means that the contrast is reduced. Although this reduced contrast is not a problem itself as long as the minimum is reasonably low, a serious consequence of the non-planarity of the mirror is that the phase of the reflected light changes. This can be seen in detail in FIG. 7 showing the complex amplitude of the reflected light. Corresponding points in FIG. 6 and 7 have assigned the reference signs a to e. For a perfectly flat mirror the amplitude is always real. For the non-flat mirror, the phase is continuously changing with deflection. In particular, for the first minimum 52(b) the phase is about 90° different from the phase in the maximum 50(a), which is zero. In perfect focus, i.e., when the surface to be patterned is perfectly within focus this change of the phase would cause a minor shift in CD, which still could be accounted for. However, when leaving the focus, a first order change of the CD occurs, when compared to the second order effect for a flat pixel. Since the focus can only be finitely accurate, the CD control in a pattern generator is very limited.
FIGS. 8 and 9 are Bossung-plots of the CD versus a defocusing parameter. The defocusing parameter describes the relative deviation from the focus (defocusing parameter=0). FIGS. 8 and 9 show groups of curves for different doses, wherein the dose is the integral of the intensity over the exposure time. FIG. 8 shows the Bossung-plot for an ideally planar micro-mirror. The curves show no skew, i.e., a good control of the CD. When going through focus, the change of the CD is a second-order effect. FIG. 9 shows the Bossung-plot for a badly non-planar pixel. The graphs show a pronounced skew, which is a first-order change of the CD with defocus.